A tangent is a line describing a curve’s direction at a point. For a symmetric quadratic Bézier curve, the tangent parallel to the endpoint segment lies halfway between that segment and the control point. section 15.4.4
Tangents support Bézier intersection testing by helping to:
- Find vertical and horizontal turning points. section 15.4.4
- Split curves into monotonic sections that can be approximated with segments. section 15.4.4
Using tangents during subdivision
When two quadratic Bézier curves have overlapping bounding boxes, compute axis-parallel tangents and split each curve at those points. Compare only overlapping sections, then halve sections until segment approximation meets the chosen error threshold.
